{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 15: Classifying data with logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from matplotlib import cm\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_function(f,xmin,xmax,**kwargs):\n",
    "    ts = np.linspace(xmin,xmax,1000)\n",
    "    plt.plot(ts,[f(t) for t in ts],**kwargs)\n",
    "    \n",
    "def scalar_field_heatmap(f,xmin,xmax,ymin,ymax,xsteps=100,ysteps=100):\n",
    "    fig = plt.figure()\n",
    "    fig.set_size_inches(7,7)\n",
    "    fv = np.vectorize(f)\n",
    "    X = np.linspace(xmin, xmax, xsteps)\n",
    "    Y = np.linspace(ymin, ymax, ysteps)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    z = fv(X,Y)\n",
    "    fig, ax = plt.subplots()\n",
    "    c = ax.pcolormesh(X,Y,z, cmap='plasma')\n",
    "    ax.axis([X.min(), X.max(), Y.min(), Y.max()])\n",
    "    fig.colorbar(c, ax=ax)\n",
    "    \n",
    "def plot_scalar_field(f,xmin,xmax,ymin,ymax,xsteps=100,ysteps=100,c=None,cmap=cm.coolwarm,alpha=1,antialiased=False, zorder=0):\n",
    "    fig = plt.gcf()\n",
    "    fig.set_size_inches(7,7)\n",
    "    ax = fig.gca(projection='3d')\n",
    "\n",
    "    fv = np.vectorize(f)\n",
    "    \n",
    "    # Make data.\n",
    "    X = np.linspace(xmin, xmax, xsteps)\n",
    "    Y = np.linspace(ymin, ymax, ysteps)\n",
    "    X, Y = np.meshgrid(X, Y)\n",
    "    Z = fv(X,Y)\n",
    "\n",
    "    # Plot the surface.\n",
    "    surf = ax.plot_surface(X, Y, Z, cmap=cmap,color=c,alpha=alpha,\n",
    "                           linewidth=0, antialiased=antialiased, zorder=zorder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 15.1 Testing a classification function on real data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bmw_finder(mileage,price):\n",
    "    if price > 25000:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.1.1 Loading the car data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from car_data import bmws, priuses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_car_data = []\n",
    "for bmw in bmws:\n",
    "    all_car_data.append((bmw.mileage,bmw.price,1))\n",
    "for prius in priuses:\n",
    "    all_car_data.append((prius.mileage,prius.price,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " (71000.0, 12500.0, 0)]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_car_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.1.1 Testing the classification function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_classifier(classifier, data):\n",
    "    trues = 0\n",
    "    falses = 0\n",
    "    for mileage, price, is_bmw in data:\n",
    "        if classifier(mileage, price) == is_bmw: #1\n",
    "            trues += 1\n",
    "        else:\n",
    "            falses += 1 #1\n",
    "    return trues / (trues + falses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.59"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_classifier(bmw_finder, all_car_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.1.3 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Update the `test_classifier` function to print the number of true positives, true negatives, false positives, and false negatives.  Printing these for the `bmw_finder` classifier, what can you tell about the performance of the classifier?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_classifier(classifier, data, verbose=False): #1\n",
    "    true_positives = 0 #2\n",
    "    true_negatives = 0\n",
    "    false_positives = 0\n",
    "    false_negatives = 0\n",
    "    for mileage, price, is_bmw in data:\n",
    "        predicted = classifier(mileage,price)\n",
    "        if predicted and is_bmw: #3\n",
    "            true_positives += 1\n",
    "        elif predicted:\n",
    "            false_positives += 1\n",
    "        elif is_bmw:\n",
    "            false_negatives += 1\n",
    "        else:\n",
    "            true_negatives += 1\n",
    "            \n",
    "    if verbose:        \n",
    "        print(\"true positives %f\" % true_positives) #4\n",
    "        print(\"true negatives %f\" % true_negatives)\n",
    "        print(\"false positives %f\" % false_positives)\n",
    "        print(\"false negatives %f\" % false_negatives)\n",
    "            \n",
    "    return (true_positives + true_negatives) / len(data) #5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true positives 18.000000\n",
      "true negatives 100.000000\n",
      "false positives 0.000000\n",
      "false negatives 82.000000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.59"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_classifier(bmw_finder,all_car_data,verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Find a way to update the `bmw_finder` function slightly to improve its performance, and use the `test_classifier` function to confirm that your improved function has better than 59% accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bmw_finder2(mileage,price):\n",
    "    if price > 20000:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.735"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_classifier(bmw_finder2, all_car_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 15.2 Picturing a decision boundary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.2.1 Picturing the space of cars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(ds):\n",
    "    plt.scatter([d[0] for d in ds if d[2]==0],[d[1] for d in ds if d[2]==0],c='C1')\n",
    "    plt.scatter([d[0] for d in ds if d[2]==1],[d[1] for d in ds if d[2]==1],c='C0',marker='x')\n",
    "    plt.ylabel(\"Price ($)\",fontsize=16)\n",
    "    plt.xlabel(\"Odometer (mi)\",fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(all_car_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(all_car_data)\n",
    "plot_function(lambda x: 25000, 0, 200000, c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(all_car_data)\n",
    "plot_function(lambda x: 21000 - 0.07 * x, 0, 200000, c='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.2.3 Implementing the classification function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decision_boundary_classify(mileage,price):\n",
    "    if price > 21000 - 0.07 * mileage:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.805"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_classifier(decision_boundary_classify, all_car_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.2.4 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini-project:** What is the decision boundary of the form $p = constant$ giving the best classification accuracy on the test data set?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constant_price_classifier(cutoff_price):\n",
    "    def c(x,p):\n",
    "        if p > cutoff_price:\n",
    "            return 1\n",
    "        else:\n",
    "            return 0\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cutoff_accuracy(cutoff_price):\n",
    "    c = constant_price_classifier(cutoff_price)\n",
    "    return test_classifier(c,all_car_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17998.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_prices = [price for (mileage,price,is_bmw) in all_car_data]\n",
    "max(all_prices,key=cutoff_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.795"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_classifier(constant_price_classifier(17998.0), all_car_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 15.3 Framing classification as a regression problem\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.3.1 Scaling the raw car data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_scale(data):\n",
    "    min_val = min(data) #1\n",
    "    max_val = max(data)\n",
    "    def scale(x): #2\n",
    "        return (x-min_val) / (max_val - min_val)\n",
    "    def unscale(y): #3\n",
    "        return y * (max_val - min_val) + min_val\n",
    "    return scale, unscale #4\n",
    "\n",
    "price_scale, price_unscale = make_scale([x[1] for x in all_car_data]) #5\n",
    "mileage_scale, mileage_unscale = make_scale([x[0] for x in all_car_data])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaled_car_data = [(mileage_scale(mileage), price_scale(price), is_bmw) \n",
    "                    for mileage,price,is_bmw in all_car_data]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(scaled_car_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.3.2 Measuring BMWness of a car"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(scaled_car_data)\n",
    "plot_function(lambda x: 0.56 - 0.35*x,0,1,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(lambda x,p: p + 0.35*x - 0.56, 0, 1,0,1)\n",
    "plt.ylabel('Price', fontsize=16)\n",
    "plt.xlabel('Mileage', fontsize=16)\n",
    "plot_function(lambda x: 0.56-0.35*x,0,1,c='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.3.3 Introducing the sigmoid function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import exp\n",
    "def sigmoid(x):\n",
    "    return 1 / (1+exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(sigmoid,-5,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.3.4 Composing the sigmoid function with other functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x,p):\n",
    "    return p + 0.35 * x - 0.56\n",
    "\n",
    "def l(x,p):\n",
    "    return sigmoid(f(x,p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 504x504 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalar_field_heatmap(l, 0, 1,0,1)\n",
    "# plot_data(scaled_car_data,white=True)\n",
    "plt.ylabel('Price', fontsize=16)\n",
    "plt.xlabel('Mileage', fontsize=16)\n",
    "plot_function(lambda x: 0.56-0.35*x,0,1,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(l, -5, 5, -5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(f,-5,5,-5,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.3.4 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Find a function $h(x)$ such that large positive values of $x$ cause $h(x)$ to be very close to $0$, large negative values of $x$ cause $h(x)$ to be very close to $1$, and $h(3) = 0.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def h(x):\n",
    "    return sigmoid(3-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iH6NCFzkKV0wsw2fG42/rLF0Sjwpd5CgMzsvgU2MG8VRVDQfaNL+LJBYVushRunpKOfVNbfz13a1eRxH5CBW6yFGaMryAEwbm8OhbG72OIvIRKnSRo2RmXD25nGW1DSyrqfc6jsghKnSRY/C5CcVkBf08qsUvJIGo0EWOQW5GGp8bX8xfNL+LJBAVusgxujo6v8vvF2l+F0kMKnSRY3RofpcF1YQ1v4skABW6yHG4ako51bubePX9Oq+jiKjQRY7HtLGDKcxJ5zHN7yIJQIUuchyCAR+zJpbyjzU7qNmt+V3EWyp0keN0xaSD87tUex1FUpwKXeQ4DcnL5ILRA3lqYbXmdxFPqdBF4uCaKRXsaWpj3nLN7yLeUaGLxMHUEQUML8rmEb05Kh5SoYvEwcH5XZbW1LO8tsHrOJKiVOgicfL5CSVkpvl5dMFGr6NIilKhi8RJXmYal4wfyjNLt9DQ1OZ1HElBKnSROLpqsuZ3Ee+o0EXiaOzQPE4r789jCzZpfhfpdSp0kTi7Zko5G3c18dq6nV5HkRQTU6Gb2TQzW2Nm68zstiMcd6mZOTOrjF9Ekb5l2kmDKcgO8qiGMEov67bQzcwP3AdcCIwBZpnZmC6O6wfcArwd75AifUl6wM/MiaX8473t1O7R/C7Se2I5Q58IrHPOrXfOtQJPAjO6OO7fgZ8AB+KYT6RPumJSOQC/0/wu0otiKfRioONb9rXRbYeY2QSg1Dn37JGeyMxuMLMqM6uqq9P80ZK8ivMzOX/0IJ5aWENLSPO7SO847jdFzcwH/Az4dnfHOudmO+cqnXOVRUVFx/vSIgnt6snl7Gps5bnl27yOIikilkLfDJR2eFwS3XZQP+Ak4BUz2whMBubqjVFJdWeeUMiwwmwefmuj11EkRcRS6AuBkWY2zMyCwExg7sGdzrkG51yhc67COVcBLACmO+eqeiSxSB/h8xnXTClnSXU9S6r3eB1HUkC3he6cCwE3Ac8Dq4E5zrmVZvZjM5ve0wFF+rLLKkvplxHgN69v8DqKpIBALAc55+YB8zptu/0wx557/LFEkkNOeoArJpbxwOsbqN3TREn/LK8jSRLTJ0VFeti1UysAePjNjZ7mkOSnQhfpYUPzM/nMuCE8+U4N+w5oFkbpOSp0kV7wlbOGsa8lxJyqWq+jSBJToYv0gpNL8plYMYDfvrGBUHvY6ziSpFToIr3k+rOGUbunmRdWbfc6iiQpFbpIL7lg9CDKC7J44LX1XkeRJKVCF+klfp9x3RnDWFxdT9XG3V7HkSSkQhfpRZdVltA/K41fvfKB11EkCanQRXpRVjDAdWcM4x/v7WDVlr1ex5Eko0IX6WXXTKkgO+jn/ld1li7xpUIX6WV5WWlcNbmcZ9/dwsadjV7HkSSiQhfxwPVnDiPg9/Hr+RrxIvGjQhfxwMDcDC47rYQ/LKpl+16t2ijxoUIX8ciNZ48gFA5rXLrEjQpdxCNlBVlMP2Uojy2oZuf+Fq/jSBJQoYt46ObzR9ISaufXGvEicaBCF/HQiKIcLhlfzCNvbWKHrqXLcVKhi3jsG+eNJBR2Gpcux02FLuKxisJsLp1QzONvV7O1odnrONKHqdBFEsDN540kHHb86mWdpcuxU6GLJIDSAVlcVlnKkwurqdnd5HUc6aNU6CIJ4ubzTsBnxl0vrPE6ivRRKnSRBDE0P5PrzhzGn5duYXltg9dxpA9SoYskkK+fO4L+WWn857zVOOe8jiN9jApdJIHkZqTxjfNH8tb6Xbyyps7rONLHqNBFEsyVk8opL8jizudW0x7WWbrEToUukmCCAR/f+fQo1m7fz5yqGq/jSB+iQhdJQBeNG0xleX9++vwaGpravI4jfYQKXSQBmRk/mjGW+qZW7npRwxglNip0kQQ1dmgeV00u57EFm1i5RcMYpXsxFbqZTTOzNWa2zsxu62L/rWa2yszeNbOXzKw8/lFFUs+3P/kJ+mcFuf2ZlRrGKN3qttDNzA/cB1wIjAFmmdmYToctASqdcycDTwP/He+gIqkoLyuNf502ikWb9vD0olqv40iCi+UMfSKwzjm33jnXCjwJzOh4gHPuZefcwQkoFgAl8Y0pkrq+cFoJp5X35z/mraZun1Y2ksOLpdCLgY5jp2qj2w7neuC54wklIh/y+YyfXDqOppZ27pi70us4ksDi+qaomV0FVAI/Pcz+G8ysysyq6ur0KTiRWJ0wsB+3XDCSZ5dv5W8rtnkdRxJULIW+GSjt8Lgkuu0jzOwC4PvAdOdcl78XOudmO+cqnXOVRUVFx5JXJGXdcPZwxgzJ5YfPrNDYdOlSLIW+EBhpZsPMLAjMBOZ2PMDMxgO/JlLmO+IfU0TS/D7++wsns7uxlTv+oksv8nHdFrpzLgTcBDwPrAbmOOdWmtmPzWx69LCfAjnA781sqZnNPczTichxOKk4j5vPO4E/LdnMM0s/9ouypDjzamxrZWWlq6qq8uS1RfqyUHuYmbMXsGbbPubdchalA7K8jiS9yMwWOecqu9qnT4qK9DEBv4+fzzwVDG55cgmh9rDXkSRBqNBF+qCS/ln8x+fGsbi6nnteet/rOJIgVOgifdT0U4byxcoS7v3HOl5ctd3rOJIAVOgifdiPZ5zEySV53PrUUj6o2+91HPGYCl2kD8tI83P/VaeRFvBx46OL2N8S8jqSeEiFLtLHFedn8stZ41lft59vPbVUy9alMBW6SBKYekIh/3bxWF5ctZ0f/UVT7aaqgNcBRCQ+rp1aweb6ZmbPX09xfiY3njPC60jSy1ToIknktmmj2FLfzJ3PvcfgvAxmnHqkiVEl2ajQRZKIz2fc9cVT2Lm/hVvnLCPo93HhuCFex5JeomvoIkkmPeDngWtP59TSfG5+Yomm200hKnSRJJSTHuChL5/OuJI8bvrdYl5YqVJPBSp0kSTVLyONh6+byNjiPL7++GLmVNV0/03Sp6nQRZJYbkYaj39lElNHFPCdp9/lvpfXaUhjElOhiyS5nPQAv7n2dGacOpSfPr+G259ZSZtmaExKGuUikgKCAR93f/FUBuVmMHv+etZu38d9V06gMCfd62gSRzpDF0kRPp/xvYtGc/flp7C0pp6L732dZTX1XseSOFKhi6SYz40v4Q9fn4rPjC/875v8+tUPNP9LklChi6Sgk4rz+OvNZ3L+qEHc+dx7XPnAAjbXN3sdS46TCl0kRfXPDnL/VRP46RdOZnltA5++ez4PvbFBZ+t9mApdJIWZGZdVlvLcLWczviyfO/6yikvue4PltQ1eR5NjoEIXEcoKsnjkuoncO2s82/YeYPp9r/Otp5ZSs7vJ62hyFDRsUUSAyNn6xacM5ZxPFHH/Kx/w4OsbePbdrVw1uZyvnTucgf0yvI4o3TCvPjVWWVnpqqqqPHltEene1oZmfv7i+/x+UQ0Bv49LJ5Rw49nDqSjM9jpaSjOzRc65yi73qdBF5Eg27Gxk9vz1/GFRLW3hMBeMHsQVk8o4e2QRfp95HS/lqNBF5Ljt2HeAh97YyFMLa9jV2EpxfiaXn17KJacWU1aQ5XW8lKFCF5G4aQm18+Kq7Tz5Tg2vr9sJwLjiPD5z8hA+M24IpQNU7j1JhS4iPaJmdxPPrdjKs+9uZVl0qOPIgTmcfWIR55xYxMRhA8hI83ucMrmo0EWkx9XsbuL5ldt4dW0db2/YTWsoTHrAx/iyfE4r789p5f0ZX9qf/tlBr6P2aSp0EelVza3tvL1hF/PX7qRq025Wbtl76BOowwuzGT00l9GD+zFqcC6jhvSjOD8TM73BGosjFbrGoYtI3GUG/Zz7iYGc+4mBQKTg362tZ1H1HpZW17NicwPPvrv10PH90gNUFGZTVpBF+YAsKgoi98sGZFHUL500vz4DGYuYCt3MpgH3AH7gAefcf3Xanw48ApwG7AIud85tjG9UEemrMoN+Jg0vYNLwgkPb9reEWLNtH+9t28uabfvYuKuJlZsbeH7FNkId5pMxg8KcdAblpjOoXwYDczMYlJtOYU46/bOC9M9KIy8rjf5ZQfKz0shM86fs2X63hW5mfuA+4JNALbDQzOY651Z1OOx6YI9z7gQzmwn8BLi8JwKLSHLISQ8curbeUag9zJb6A2za3UjN7ma27T3Ajr0H2L73AFsaDrC0pp5dja2Hfd5gwEd+Zho5GQGygwGy0/1kBwNkpQfISfeTFQyQHfSTnR4gM+gn6PcRDPhID/gJBg7ej9wG/T4y0nwE/R/u8/sMv88IRG/9ZvgSZDx+LGfoE4F1zrn1AGb2JDAD6FjoM4A7ovefBn5pZua0eKGIHKWA3xe53HKEse2toTC7G1upb25lT2MbDc2t7GlqY09TKw3R28aWdhpbQzS1tLNt7wEaW0I0trbTFL2NJzMI+AyfRYred6jwffh9EPB9+A+Bz+CbF5zIxacMjWsGiK3Qi4GOy4XXApMOd4xzLmRmDUABsLPjQWZ2A3ADQFlZ2TFGFpFUFwz4GJyXweC8Y5tfJhx2NLe109zWTmsoTEsoTOvBr/Z2WtrCtLSHP74v1E67g/ZwmPZw5DYUdoTDjlDY0R79OnTfOdrbo7fR7eGwIz8rLc5/IxG9+qaoc242MBsio1x687VFRA7y+Yzs9ADZ6ck1LiSWt443A6UdHpdEt3V5jJkFgDwib46KiEgviaXQFwIjzWyYmQWBmcDcTsfMBa6N3v8C8A9dPxcR6V3d/r4RvSZ+E/A8kWGLDzrnVprZj4Eq59xc4DfAo2a2DthNpPRFRKQXxXQByTk3D5jXadvtHe4fAC6LbzQRETka+viViEiSUKGLiCQJFbqISJJQoYuIJAnPps81szpgkycv3rVCOn2yNcEkej5I/IyJng8SP2Oi54Pkz1junCvqaodnhZ5ozKzqcHMMJ4JEzweJnzHR80HiZ0z0fJDaGXXJRUQkSajQRUSShAr9Q7O9DtCNRM8HiZ8x0fNB4mdM9HyQwhl1DV1EJEnoDF1EJEmo0EVEkoQKvRMz+7aZOTMr9DpLZ2b2UzN7z8zeNbM/mVm+15kgsoi4ma0xs3VmdpvXeTozs1Ize9nMVpnZSjO7xetMXTEzv5ktMbO/ep2lK2aWb2ZPR38GV5vZFK8zdWZm34r+N15hZk+Y2bEtaRS/PA+a2Q4zW9Fh2wAze9HM3o/e9j/ScxwNFXoHZlYKfAqo9jrLYbwInOScOxlYC3zX4zwdFxG/EBgDzDKzMd6m+pgQ8G3n3BhgMvD/EjAjwC3Aaq9DHME9wN+cc6OAU0iwrGZWDHwDqHTOnURkum+vp/J+CJjWadttwEvOuZHAS9HHcaFC/6i7ge8ACflOsXPuBedcKPpwAZHVo7x2aBFx51wrcHAR8YThnNvqnFscvb+PSBEVe5vqo8ysBPgM8IDXWbpiZnnA2UTWPsA51+qcq/c2VZcCQGZ05bQsYIuXYZxz84msEdHRDODh6P2HgUvi9Xoq9CgzmwFsds4t8zpLjK4DnvM6BF0vIp5QZdmRmVUA44G3vU3yMT8ncjIR9jrIYQwD6oDfRi8LPWBm2V6H6sg5txn4HyK/YW8FGpxzL3ibqkuDnHNbo/e3AYPi9cQpVehm9vfotbXOXzOA7wG3d/ccHmc8eMz3iVxGeNy7pH2PmeUAfwC+6Zzb63Weg8zss8AO59wir7McQQCYANzvnBsPNBLHSwXxEL0WPYPIPz5DgWwzu8rbVEcWXaozblcEkmvJ62445y7oaruZjSPyQ7DMzCByKWOxmU10zm3rxYiHzXiQmX0J+CxwfoKs2xrLIuKeM7M0ImX+uHPuj17n6eQMYLqZXQRkALlm9phzLpHKqBaodc4d/M3maRKs0IELgA3OuToAM/sjMBV4zNNUH7fdzIY457aa2RBgR7yeOKXO0A/HObfcOTfQOVfhnKsg8sM7obfLvDtmNo3Ir+XTnXNNXueJimURcU9Z5F/p3wCrnXM/8zpPZ8657zrnSqI/ezOJLLKeSGVO9P+FGjP7RHTT+cAqDyN1pRqYbGZZ0f/m55Ngb9xGzQWujd6/FngmXk+cUmfoSeCXQDrwYvQ3iQXOua95Gehwi4h7makLZwBXA8vNbGl02/eia+VK7G4GHo/+w70e+LLHeT7COfe2mT0NLCZySXIJHnx6Ty4AAABRSURBVE8DYGZPAOcChWZWC/wb8F/AHDO7nsgU4l+M2+slxm/tIiJyvHTJRUQkSajQRUSShApdRCRJqNBFRJKECl1EJEmo0EVEkoQKXUQkSfx/j5/U62sOGwsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(h,-5,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 15.4 Exploring possible logistic functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.4.1 Parametrizing logistic functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_logistic(a,b,c):\n",
    "    def l(x,p):\n",
    "        return sigmoid(a*x + b*p - c)\n",
    "    return l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.4.2 Measuring the quality of fit for a logistic function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_logistic_cost(a,b,c):\n",
    "    l = make_logistic(a,b,c)\n",
    "    errors = [abs(is_bmw-l(x,p)) \n",
    "              for x,p,is_bmw in scaled_car_data]\n",
    "    return sum(errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import log\n",
    "plot_function(lambda x: -log(x),0.01,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.605170185988091"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-log(0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.907755278982137"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-log(0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def point_cost(l,x,p,is_bmw): #1\n",
    "    wrong = 1 - is_bmw\n",
    "    return -log(abs(wrong - l(x,p)))\n",
    "\n",
    "def logistic_cost(a,b,c):\n",
    "    l = make_logistic(a,b,c)\n",
    "    errors = [point_cost(l,x,p,is_bmw) #2 \n",
    "              for x,p,is_bmw in scaled_car_data]\n",
    "    return sum(errors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.4.3 Testing different logistic functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_line(acoeff,bcoeff,ccoeff,**kwargs):\n",
    "    a,b,c = acoeff, bcoeff, ccoeff\n",
    "    \n",
    "    # black by default\n",
    "    if 'c' not in kwargs:\n",
    "        kwargs['c'] = 'k'\n",
    "        \n",
    "    if b == 0:\n",
    "        plt.plot([c/a,c/a],[0,1])\n",
    "    else:\n",
    "        def y(x):\n",
    "            return (c-a*x)/b\n",
    "        plt.plot([0,1],[y(0),y(1)],**kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(scaled_car_data)\n",
    "plot_line(0.35,1,0.56,)\n",
    "plot_line(1,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "130.92490748700456"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logistic_cost(0.35,1,0.56)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "135.56446830870456"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logistic_cost(1,1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.4.4 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Implement the function `plot_line(a,b,c)` referenced in the chapter that plots the line $ax + by = c$ where $0 \\leq x \\leq 1$ and $0 \\leq y \\leq 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution:** (see implementation above)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini-project:** What does the graph of $k(x,y) = \\sigma(x^2 + y^2 - 1)$ look like? What does the decision boundary look like, meaning the set of points where $k(x,y) = 0.5$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def k(x,y):\n",
    "    return sigmoid(x**2 + y**2 - 1)\n",
    "plot_scalar_field(k,-3,3,-3,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini-project:** Two equations $2x + y = 1$ and $4x + 2y = 2$ define the same line, and therefore the same decision boundary.  Are the logistic functions $\\sigma(2x + y - 1)$ and $\\sigma(4x + 2y - 2)$ the same?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(lambda x,y:sigmoid(2*x+y-1),-3,3,-3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(lambda x,y:sigmoid(4*x+2*y-2),-3,3,-3,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 15.5 Finding the best logistic function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.5.1 Gradient descent in three dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def length(v):\n",
    "    return sqrt(sum([vi*vi for vi in v]))\n",
    "\n",
    "def secant_slope(f,xmin,xmax):\n",
    "    return (f(xmax) - f(xmin)) / (xmax - xmin)\n",
    "\n",
    "def approx_derivative(f,x,dx=1e-6):\n",
    "    return secant_slope(f,x-dx,x+dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_gradient(f,x0,y0,dx=1e-6):\n",
    "    partial_x = approx_derivative(lambda x:f(x,y0),x0,dx=dx)\n",
    "    partial_y = approx_derivative(lambda y:f(x0,y),y0,dx=dx)\n",
    "    return (partial_x,partial_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_gradient3(f,x0,y0,z0,dx=1e-6):\n",
    "    partial_x = approx_derivative(lambda x:f(x,y0,z0),x0,dx=dx)\n",
    "    partial_y = approx_derivative(lambda y:f(x0,y,z0),y0,dx=dx)\n",
    "    partial_z = approx_derivative(lambda z:f(x0,y0,z),z0,dx=dx)\n",
    "    return (partial_x,partial_y,partial_z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent3(f,xstart,ystart,zstart,\n",
    "                      tolerance=1e-6,max_steps=1000):\n",
    "    x = xstart\n",
    "    y = ystart\n",
    "    z = zstart\n",
    "    grad = approx_gradient3(f,x,y,z)\n",
    "    steps = 0\n",
    "    while length(grad) > tolerance and steps < max_steps:\n",
    "        x -= 0.01 * grad[0]\n",
    "        y -= 0.01 * grad[1]\n",
    "        z -= 0.01 * grad[2]\n",
    "        grad = approx_gradient3(f,x,y,z)\n",
    "        steps += 1\n",
    "    return x,y,z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.5.2 Using gradient descent to find the best fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.21114493148496014, 5.045439728207488, 2.1260122566471376)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent3(logistic_cost,1,1,1,max_steps=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8845715265377516, 6.65754318727634, 2.9550572849988455)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent3(logistic_cost,1,1,1,max_steps=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make a cool graph of the decision boundary moving as gradient descent runs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(scaled_car_data)\n",
    "for i in range(0,1000,100):\n",
    "    a,b,c = gradient_descent3(logistic_cost,1,1,1,max_steps=i)\n",
    "    plot_line(a,b,c,alpha=i/1000,c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.7167003088210118, 11.422062406779267, 5.596878365032182)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent3(logistic_cost,1,1,1,max_steps=8000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(scaled_car_data)\n",
    "plot_line(0.35,1,0.56)\n",
    "plot_line(3.7167003153580045, 11.422062409195114, 5.596878367305919)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.5.3 Testing an understanding the best logistic classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def best_logistic_classifier(x,p):\n",
    "    l = make_logistic(3.7167003153580045, 11.422062409195114, 5.596878367305919)\n",
    "    if l(x,p) > 0.5:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_classifier(best_logistic_classifier,scaled_car_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(make_logistic(0.35,1,0.56), -2, 2, -2, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scalar_field(make_logistic(3.7167003153580045, 11.422062409195114, 5.596878367305919), -2, 2, -2, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15.5.5 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Modify the `gradient_descent3` function to print out the total number of steps taken before it returns its result.  How many steps does the gradient descent take to converge for `logistic_cost`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent3(f,xstart,ystart,zstart,tolerance=1e-6,max_steps=1000):\n",
    "    x = xstart\n",
    "    y = ystart\n",
    "    z = zstart\n",
    "    grad = approx_gradient3(f,x,y,z)\n",
    "    steps = 0\n",
    "    while length(grad) > tolerance and steps < max_steps:\n",
    "        x -= 0.01 * grad[0]\n",
    "        y -= 0.01 * grad[1]\n",
    "        z -= 0.01 * grad[2]\n",
    "        grad = approx_gradient3(f,x,y,z)\n",
    "        steps += 1\n",
    "    print(steps)\n",
    "    return x,y,z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7243\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(3.7167003088210118, 11.422062406779267, 5.596878365032182)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent3(logistic_cost,1,1,1,max_steps=8000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini project:** Write an `approx_gradient` function that can calculate the gradient of a function in any number of dimensions.  Then write a `gradient_descent` function that works in any number of dimensions.  To test your `gradient_descent` on an $n$-dimensional function, you can try a function like $f(x_1,x_2, \\ldots ,x_n) = (x_1 - 1)^2 + (x_2 - 1)^ + \\ldots + (x_n - 1)^2$ where $x_1, x_2, \\ldots , x_n$ are the $n$ input variables to the function $f$.  The minimum of this function should be $(1,1, \\ldots , 1)$, an $n$-dimensional vector with 1 in every entry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "def partial_derivative(f,i,v,**kwargs):\n",
    "    def cross_section(x):\n",
    "        arg = [(vj if j != i else x) for j,vj in enumerate(v)]\n",
    "        return f(*arg)\n",
    "    return approx_derivative(cross_section, v[i], **kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_gradient(f,v,dx=1e-6):\n",
    "    return [partial_derivative(f,i,v) for i in range(0,len(v))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(f,vstart,tolerance=1e-6,max_steps=1000):\n",
    "    v = vstart\n",
    "    grad = approx_gradient(f,v)\n",
    "    steps = 0\n",
    "    while length(grad) > tolerance and steps < max_steps:\n",
    "        v = [(vi - 0.01 * dvi) for vi,dvi in zip(v,grad)]\n",
    "        grad = approx_gradient(f,v)\n",
    "        steps += 1\n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_squares(*v):\n",
    "    return sum([(x-1)**2 for x in v])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0000002235452137,\n",
       " 1.0000002235452137,\n",
       " 1.0000002235452137,\n",
       " 1.0000002235452137,\n",
       " 1.0000002235452137]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = [2,2,2,2,2]\n",
    "gradient_descent(sum_squares,v)"
   ]
  }
 ],
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